Solve for area of A1 when volume and A2 are known for a frustum pyramid

Question

I'm wondering how to solve out the equation so that A1 is on the left side of the equation when the volume and A2 are known. Any thoughts?

$V=\left ( \frac{h}{3} \right )*\left ( A_{1}+A_{2}+\sqrt{A_{1}*A_{2}} \right)$

I guess $h$ is known as well. Isn't this a quadratic in $A_1$? — Patricio, Mar 24 '21 at 17:16
Yes, H is known as well. I'm a little rusty with solving out equations so I wasn't sure how to pull A1 out. — EngineeringSam, Mar 24 '21 at 17:20

score 0 · Answer 1 · answered Mar 24 '21 at 18:47

HINT: Here are steps to remove the square root sign

$V=\frac{h}{3}(A_1+A_2+\sqrt{A_1A_2})$

$\frac{3V}{h}=(A_1+A_2+\sqrt{A_1A_2})$

$\frac{3V}{h}-A_1-A_2=\sqrt{A_1A_2}$

$(\frac{3V}{h}-A_1-A_2)^2=A_1A_2$

$(\frac{3V}{h})^2+A_1^2+A_2^2+2(A_1A_2+\frac{3V}{h}A_1+\frac{3V}{h}A_2)=A_1A_2$

The above is a quadratic equation about $A_1$ and hope you can continue now.

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